muEC::PART::Part2ListHook

muEC::PART::Part2ListHook – hook lengths of partitions

Computes the list of hook lengths of a partition

→ Examples

Calls:

muEC::PART::Part2ListHook(part)

muEC::PART::Part2ListHook(part, a)

muEC::PART::Part2ListHook(part, q, t)

Parameters:

part:

any list denoting a partition

Related Functions:

muEC::PART::ListPart, muEC::PART::Part2Border, muEC::PART::Part2Conjugate, muEC::PART::Part2Diagonal, muEC::PART::Part2Mat, muEC::TYP::IsPart

Details:

The muEC::PART::Part2ListHook function computes the list of all hook lengths of a given partition. The result is sorted into non-increasing order.

The arm and leg length of a cell are respectively and where is the conjugate of .

The call muEC::PART::Part2ListHook(part, a) computes the Jack-hook-product. a may be any expression. This is the product over all cells of the diagram of the partition part.

The call muEC::PART::Part2ListHook(part, q, t) computes the two-variable hook polynomial. The arguments q and t can be any expressions. This is the product over all cells of the diagram of the partition part.

Example 1:

muEC::PART::Part2ListHook( [3,1] );

4! / _mult( op(%) );

muEC::PART::Part2ListHook( [2,1], z );

muEC::PART::Part2ListHook( [2,1], z, t );